Euthyphro Dilemmas as Mathematical Objects

introduction to series ii

introduction to series ii

I

This blog has recently been grasping at the notion of values, either directly or by reference to nihilism. I’ve mostly failed, because I need vocabulary that I don’t really have, because the question isn’t really the question it looks like. This is an oldnew question, in precisely the way that most things are oldnew questions.

This is the old form of it: Socrates asks Meno what virtue is. Meno, reasonably, replies with a list of actions that are good things to do. Socrates, reasonably, answers that there must be some essence of “virtue” that connects all of these things, a value or judgment or faculty of judgment that determines the “good” from the “bad.”

No one can figure it out, which leads to the Meno problem. The Meno problem is this:

A man cannot search either for what he knows or for what he does not know. He cannot search for what he knows–since he knows it, there is no need to search–nor for what he does not know, for he does not know what to look for.

So, it seems that knowing virtue is impossible. Socrates then leading-questions a slave boy into doing geometry, which proves something about inborn knowledge, and Socrates suggests that knowing things maybe comes from reincarnation. Kind of. Either way, knowledge of “virtue” is, at least plausibly, as objectively valid as mathematics. To really drive the point home, Socrates relays a series of poetic invocations of the gods and tells a myth about the afterlife. Meno asks him how true any of that is, and Socrates responds by saying “Eh.” and also “We’ll be better men if we think it is, because it will make us brave enough to question things.”

This is really weird. It’s not obvious that math is anything like virtue. Moreover, it’s not clear that math is itself objective, which is underlined by the fact that it’s reliant on a mythical interpretation that presupposes its own existence. Finally, Socrates forces acquiescence by calling it “better” to believe in true knowledge, but the point about not knowing about knowing is that it means you can’t tell what’s “better” and what’s “worse.”

Plato is a motherfucker, he does have a point, I’m ignoring it, moving on.

II

“Phil 101 and the Cave, etc.” I know, Reloaded and Revolutions really killed the franchise, but bear with me here.

This next series is going to be on epistemology. This is the introduction, just like the old one had an introduction, and that introduction still applies: it’s about nihilism and modernity, and it’s going to connect with politics and narcissism and values and meaning. Unlike the old series, it’s going to take me a bit to get there. The first series had a bunch of stuff we can agree on, like “Politics are things people do, sometimes with ballots and other times with guns.” This one is going to have a lot we don’t agree on, like “Actually, it makes perfect sense for Heidegger to talk about the world worlding, really clarified the passage for me.”

The reason it makes sense is math.

The “worlding” school of philosophy, i.e. continental philosophy, where “continent”=France and “philosophy”=[tasteless joke at the expense of the dead], is generally considered to be the one that tacitly endorses neo-Kipling verses like “The scientific method is a social construct, foisted on hapless Natives by monopoly men in Pith helmets, haven’t you read post-colonial theory?” Dazzlingly incoherent, and also why it’s going to sound odd when I say that they’re part of a tradition that was all about the problem of saving math as a reliable thing.

They’re responding to Heidegger, who is responding to Husserl, both of whom are dealing with Kant’s framework, and Kant’s framework doesn’t make any sense until you realize that he needs the entire thing to address one central issue: why does math work with the physical world?

As shocking as this sounds to people who dismiss continental philosophy as inherently anti-rational, I guarantee it’s more shocking to people heavily invested in post-Heideggerian Comparative Literature departments.

III

This is the short form.

Hume comes shrieking down the mountain and wrecks everything via skeptical empiricism, which leads to this:

But what have I here said, that reflections very refined and metaphysical have little or no influence upon us? This opinion I can scarce forbear retracting, and condemning from my present feeling and experience. The intense view of these manifold contradictions and imperfections in human reason has so wrought upon me, and heated my brain, that I am ready to reject all belief and reasoning, and can look upon no opinion even as more probable or likely than another. Where am I, or what? From what causes do I derive my existence, and to what condition shall I return? Whose favour shall I court, and whose anger must I dread? What beings surround me? and on whom have, I any influence, or who have any influence on me? I am confounded with all these questions, and begin to fancy myself in the most deplorable condition imaginable, invironed with the deepest darkness, and utterly deprived of the use of every member and faculty.

This is bad for several reasons, but the worst part is how to deal with the concept “several.”

Included in the wreckage is geometry, because empiricism. Algebra and arithmetic are not, which is extremely confusing, and Hume has no decent way to address that (his attacks on geometry are also kind of contradictory). Either way, even if those are saved, it’s not clear why they should be. That is, if all our faculties are too flawed to have any value re: truth, then how does math somehow make the cut? As in: where did it come from?

This leads to a second problem: why should they work with the outside world? It’s, I guess, intelligible to assume that maybe we’re just “lucky” or something, but that still leaves us with the fact that all of our other senses are bullshit. The fact that we can reapply mathematics to make airplanes fly, despite all the components of airplanes being subject to human frailty and untruth, is pretty weird.

On way to address the problem is to consider it almost like the Euthyphro dilemma. The dilemma is originally over “piety” or “goodness.” It goes: “Does God command it because it is good, or is it good because God commands it?” i.e. is goodness inherent to the world and God judges accordingly, or is “God” our only measure for some arbitrary goodness. The mathematical version is: “Does math fit physics because the physical world is mathematical, or does math fit physics because our nature makes the physical world mathematical?”

Kant’s answer is “Yes.”

No one had ever thought of this before, and it’s convincing enough to resolve a pre-Socratic epistemological conundrum (I really need to emphasize just how rare that is philosophically.) That “Yes” saves the certainty of mathematics, our capacity to use it in the sciences, and more-or-less the practical virtues of empiricism. The problem is that Kant’s method of saving those is incredibly counterintuitive, and its implications are weird enough to lead to, well, modern phenomenology.

The analytics mostly ignored that as “weird metaphysical stuff,” ran into the problem independently, couldn’t logical positivism out of it, and have now, finally, returned to Kant. The continentals took Kant seriously, continued his tradition, at some point forgot that their school only makes sense in light of Kant, proclaimed math oppressive and/or not real.

It’s also really, unbelievably hard to try and succinctly capture Kant’s reasoning, so this is going to take some time. Anyone in modern philosophy departments feel warned, I’m not a professional, you will not stop me. Scream in the comments.

IV

The series is still primarily concerned with books I use to understand the world. But to get at why those particular books make sense, and therefore why they have anything to offer, I’m going to need to do two things: 1) try and explain why that question is important, and why its answer should make you accept otherwise alien interpretations of the world. 2) Give a super rough-shod history of the answer, focusing on the parts important for people I like.

This is not because I’m particularly gifted at philosophy, nor is it because I want to act professorial. I’m not, I won’t, don’t care. It’s because “Why does math work?” sounds like philosophy’s worst excess, right up there with “why” over and over again, which means any response is not going to be taken seriously if it sounds particularly weird. (It’s also because I don’t know of any decent writeups that aren’t as painfully obtuse as the writers themselves.) I’ve tried to avoid explicitly discussing philosophers, but that’s not really possible here.

In practical terms: the first posts are on Plato and Hume dealing with the question of mathematics (and, by extension, Gettier, Wigner, Carnap, whoever seems important, etc.). Kant is going to be a while. Heidegger and Nishitani next. Aristotle (and/or Heidegger’s use of Aristotle), and Nietzsche are going to be the end of it, with the last two transitioning this series into the next one.

I’m not going to talk about Hegel because I don’t want to. Same with all the other obvious gaps.

Since I predicted five essays for the last one and went well over that, I’m not going to make the same mistake here. “It will be an amount.” I will be interrupting this series with other posts, quite plausibly (read: certainly) the next few. This introduction serves two purposes: a) I have a bunch of drafts of things that I don’t want to finish without moving onto something else; b) I hate writing introduction posts to series (and/or this blog, the since-September planned post of which is still absent), which meant I was delaying actually writing about the things I needed to write about to write about other things I didn’t really want to be writing about.

Last one was convoluted, my bad: I hit a wall, and “get over the introduction and on with it” was the superior option.

V

Nothing I say here is going to be unique, and it’s not from me. It’s interpretations of books applied to interpretations of other books. More importantly, those books are also not saying anything unique.

The last introduction had a TLDR that was a short story. This one is, thankfully, shorter. It’s a poem, interpret accordingly, by which I mean “carefully.”

It’s probably obvious, but “dewdrops” are a traditional image of ephemerality in haiku. A “dewdrop world” is, thus, an image of our own. The moral implications are clear: this world is not something to be attached to. It is suffering and escape.

The poet Issa was a devout buddhist (specifically Pure Land), and he knew suffering. His mother died when he was young, and his father remarried the Platonic form of Disney stepmothers. His father then sent him to work in Edo, died, and left Issa fighting his step-mother in court for years. Issa married late, and his son died just after birth. Two years later, his daughter followed her brother.

After the death of his daughter (he would lose another child soon after), Issa wrote the following poem. It is true, and it’s a better version of everything I’ll need wasteful words to say.

Issa was a monk, and he knew the renunciation of this world was our own solace. His daughter died in his arms and he still knew that, but his daughter died in his arms when he knew that. He wrote:

18 thoughts on “Euthyphro Dilemmas as Mathematical Objects”

Splendid. I look forward to seeing how you handle the Transcendental Deduction. I feel like I understand it, but would be hard-pressed to give an account of it.

Incidentally, I’ve been intending to write something which I believe will end up being similar for quite a while. It’s on aesthetics, which I’ve increasingly been thinking is the single most important unresolved problem in all of human thought. I don’t believe I have a definitive answer to aesthetics, but I do think I have something that might contribute – I just don’t know quite how to convey why aesthetics are so important. The only thing I can really think to do is to walk through every philosophical problem I’ve ever wrangled with from the beginning, demonstrate the iterative solutions with footnotes to the helpful philosophers whose works I’m cribbing off of, and then see if I can make a convincing sell of the last great problem. Maybe I’ll even do it, one of these days.

The reason I mention is that by the structure of what you’re bringing in (parts include the conclusion), it looks like you’re tackling something very similar to what I have in mind, and I’m very interested in seeing what you have to say. There’s nothing quite so pleasant as seeing a serious attempt at dealing with a grade A difficult problem.

The transcendental deduction is going to be a hassle, and also kind of necessary for really obvious reasons. I know how to do a basic Kant overview, I’m still trying to figure out how to get into the technical aspects without rewriting the damn book.

I agree completely about the “aesthetics as the great problem” thing. I probably shouldn’t reveal this because everything could change, but my current plan is to do four series on… whatever it is I’m writing on. Politics -> Epistemology -> Ethics -> Aesthetics.

Realistically, those will all fall into one another. One way to tackle it, although try to do this without looking like the world’s worst Nietzsche fan boy since Michel, is to view value systems as the core of any philosophical stance, and then to view aesthetics as the root of value systems. That’s not a bad start, anyway.

I had a teacher once who was trying to talk about Greek tragedy, and all the philosophical theories that tried to account for it, and finally just said: “I think Nietzsche would say that the Greeks liked tragedy because the words were beautiful.” It’s true. Probably the same, or same enough, for everything else.

Don’t worry; the second you decided to write about Kant, you already ensured you’ll be wrong in the minds of everyone who reads you. What can be hoped for is to be wrong in an interesting way, and I look forward to it.

Of course, what I’m most interested in – with regards to aesthetics, this time – is how to treat them so that one can, as Kant says about a totally different (but also totally identical) subject:

“make an attempt to see whether we cannot successfully steer human reason between these two cliffs, assign its determinate boundaries, and still keep open the entire field of its purposeful activity.” (B128)

I’m sure you know exactly what I mean: dogmatism and nihilism. If aesthetics are the root of all – and they are – then there must be an answer as to where they come from and what validity each individual aesthetic may have. If there is a canon of true aesthetics, you end up with dogmatism, where you can only convince those who are already convinced and alienate the rest. If all aesthetics are utterly incomparable in validity, which is understandably the most popular description by far in this day and age, you get… nihilism, of course. So what’s needed, really, is something like a preterdeterminate analysis of aesthetics which refuses to shackle itself with either the recursive navalgazing of dogmatic definition or the dazed myopia of nihilism – a true metalanguage, that is, true language, which determines as much as it is determined and is pure reference rather than devolving into what is referred to. (Bertrand Russell would have been fortunate to have more exposure to interpreted programming languages during his youth – but ah, anachronisms abound). In any case, I think that’s something of what’s captured in your little tagline – “antecedents have consequences.” But it’s still nice to thoroughly describe what’s at stake.

“The first to label others as nihilists was Friedrich Heinrich Jacobi, a Counter-Enlightenment reactionary. His criticism was that of Enlightenment thought and ideals, specifically of the radical Enlightenment. It was the view that rationality unmoored from faith, as speculative reason and radical skepticism, was dangerous and would lead to meaninglessness, moral relativism, materialism, atheism, fatalism, and atomized individuality (see atheism dispute for further info).

“Jacobi was charged as being an unsystematic thinker. By stating that others were nihilists, it was his way of defending himself—in that, to his view, at least he believed in something. Belief was everything to him and so its opposite was nothingness, i.e., nihilism.”

From this perspective, either one was a fundamentalist believer or a nihilist without any belief. Calling someone a nihilist was similar to calling them an atheist, as a deist like Thomas Paine was dismissed as an atheist. Of course, most Enlightenment thinkers and early modern revolutionaries didn’t lack political and religious beliefs. But that was a convenient way to disparage them, implying their views were meaningless and irrelevant or even dangerous.

The source of the reactionary’s complaint, however, did point to a genuine issue. Enlightenment thought led to shifting the foundations of society — away from a theocratic social order toward what was more centered on humanity within the world. But as far as that goes, the same fear was perceived in the Protestant Reformation in replacing the Church’s role with a direct human relationship to God. But it was the ancien regime losing power, both during the Protestant Reformation and the Enlightenment Age, that paved the way for new kinds and contexts of meaning based on new claims of truth value and authority.

Later on, some political activists described themselves as nihilists, specifically in Russia. It wasn’t for a lack of beliefs, but their primary concern was with an oppressive system. Future possibilities were uncertain because the system had denied all other possibilities, even as the old order was weakening. So, the nihilists sought to eliminate the oppressive social and political regime, in the hope (faith?) that this would clear space for a new society to be built. Nihilism was far from apathy, either in the early modern era or later on. It actually expressed an optimism toward creating something entirely new, which is precisely what made it threatening.

“Bear in mind, though, that what I call “nihilism” is much broader than it’s normally considered: anti-natalism, Lovecraft, materialism, etc. are symptoms of it, not its standard-bearers. Nihilism is the default of society, not a theory adopted by its outcasts. Indeed: many of those outcasts who most loudly proclaim their nihilism are, in the final analysis, reactions against it.”

I hadn’t thought about it that way. The mainstream meaning of nihilism still has its original critique clinging to it. It remains more often used to dismiss someone else’s beliefs by denying they have beliefs at all. Only a minority of those accused of nihilism are likely to claim the label for themselves. Your last point is particularly relevant. The Russian nihilists from more than a century ago, as modern capitalism took ever greater hold, were most definitely reacting against what could be called the nihilism of corrupt power that served no higher ideal than power-mongering itself. It’s odd that liberals now have sometimes turned the tables on the fundamentalists in calling them nihilists, but the charge is basically the same.

The other thing that I wanted to respond to is your mentioning Hume. I would take a step back. The question that my mind returns to is what is the source of value and meaning. Hume is helpful in this regard. He helped formulate the bundle theory of mind/self in the Western tradition, although it was long preceded by Buddhist thought. I don’t fully understand your perspective. But considering that you ended on a note of Buddhism, the bundle theory seems more than relevant.

What exactly is consciousness out of which our self-experience forms? The answer to that question determines our answers to other questions. Some would see this questioning of identity as nihilistic, as it challenges the dominant paradigm of the ego theory. If neither God’s ego nor the human ego has ultimate authority, what does? And based on whatever authority is to be asserted, what will that leave us with?

I’m using the term more or less how Nietzsche uses the term (and, kind of, Strauss and Heidegger after him). I suppose the (no less vague) gloss would be “that which devalues life” or leads one to reject it. That doesn’t literally mean suicide, of course, but a kind of chipping away at meaning and action. It’s probably going to take me some time to unpack that. I’m… well, I’m pretty sure I’d call both the late autocracy of Russia and the nihilist movement “nihilistic” from that standpoint. Utopianism has a way of despising and denying the present that, by extension, rejects human nature.

I’m uncertain about, well, consciousness. It’s hard, I don’t really know if I have a coherent enough perspective to be called that. I do think that Hume opens himself up to a real problem, though. I can accept that we’re “loose parts flying in formation” but, well, all that does for me is make me wonder “why a formation, then?”

Another way of putting it: it’s dead certain that we’re a bunch of drives all competing, and that most of it is unconscious, but then why is there an experience of ego at all? It’s presumably important, and it’s certainly atomic, at least physically so (in the sense of I can never die for you, that’s all your own). It’s fine if this “ego” isn’t actually everything, and maybe it is hiding the rest. But, well, all that does is redefine ego, not rid oneself of it. Instead of “all of you” ego is now “the drive that smothers the rest and makes you think it’s all of you.” The implications are interesting, of course, but that doesn’t make it not a real thing to address. It’s just a smaller real thing to address. (This is actually Kant’s apperception that deals with the manifold, although I don’t necessarily buy his argument either.)

I think values are derived to basically corral those perceptions to the ends they determine. I have no idea where they come from. It’s a really hard problem.

” I’m pretty sure I’d call both the late autocracy of Russia and the nihilist movement “nihilistic” from that standpoint. Utopianism has a way of despising and denying the present that, by extension, rejects human nature.”

I don’t know the Russian nihilist movement all that well. They were a response to the prevailing nihilism. I’m just not sure exactly what that response was. It was maybe more of a protest movement, such as anti-war movement, than an attempt at political organizing toward some specific goal. I’m not sure what nihilists might have thought society could have looked like if they somehow had gained victory. I also don’t have a clue what those Russian nihilists thought about human nature, but I don’t get the sense that they denied it. Some of them were rationalists and materialists, which implies a certain kind of human nature.

There were anarchists among the nihilists as well. And many anarchists were seeking a more communal way of living and organizing (e.g., anarchosyndicalism). So, some of them were advocating a positive vision, whether or not one deems it utopian. It was at a time when capitalism was taking hold and the memory of feudalism lingered.

The thing about feudalism is that it offered a certain amount of decentralized power rooted in local communities. Maybe that is part of what was inspiring the nihilists, not utopianism so much as the living memory of an earlier system, the remnants of which persisted in the rural areas. They certainly didn’t want to return to feudalism, but it reminded people that other possibilities remained. Plus, the breakdown of feudalism meant the breakdown of traditional order and the weakening of traditional authority, creating the new possibility of individuals to take action and make challenges.

Just some thoughts. Anyway, I only brought it up as historical context. Nietzsche lived during that era. I’m sure he was somewhat familiar with the Russian nihilists. But during his later life, the nihilists had mostly become a term for terrorists. So, maybe what nihilists had previously been advocating was already disappearing from public awareness at that point. The demonization of nihilism was a reaction to a reaction.

“why a formation, then?”

Why not? The world is full of formations. Swarms and flocks show collective intelligence. A formation is simply a way of accomplishing something. But there is nothing essentialist abut it. Formations appear and disappear. Psychiatry is filled with what happens when certain formations breakdown or new formations take hold. And consciousness studies has gone into interesting territory in where it crosses over with cultural studies, anthropology, philology, linguistics, etc (Ong, Snell, Jaynes, McGilchrist, Luhrmann, and many others).

“Another way of putting it: it’s dead certain that we’re a bunch of drives all competing, and that most of it is unconscious, but then why is there an experience of ego at all?”

Why is there an experience of a car when you’re driving? Well, it gets you somewhere. It has a practical purpose. But when it isn’t useful the ego-sense disappears, such as during sleep or when deeply focused. The ego is a structure to be used for a purpose. So, it is real. But many things are real. The lack of ego is also real, as the mind uses all kinds of neurocognitive structures. And different cultures won’t use the exact same structures, some of them not seeming to have thick boundaried egos in the Western sense.

“It’s fine if this “ego” isn’t actually everything, and maybe it is hiding the rest. But, well, all that does is redefine ego, not rid oneself of it.”

When we are using such terms, there are very specific meanings within psychiatry, psychology, and consciousness studies. We could have a long discussion about that, as it is a vast field of study. But this probably isn’t the time or the place.

Those who like to enforce their authority onto others tend to call questioning authority nihilistic. That is the origin of the term, as it initially came to be used in the modern era. The Russian nihilists don’t seem to have been attempting reject all authority. They were specifically rejecting official authority of the church and state, in order to bring authority back down to the local level of human individuals. That would have much to say about values, of course. Individualism has become tied into a particular expression of the egoic self.

About the denial of human nature, I’ve come across some left-wingers who for ideological reasons will proclaim such a denial. This could be interpreted as utopianism, as if there is nothing within humans that can limit them. But I’ve come to the conclusion that this isn’t the case for many and maybe most of them. It more seems to be a disagreement about what human nature means. What some left-wingers buck against is the idea that there is a singular, unchanging, and deterministic human nature.

This disagreement is what motivates, for example, the conflict between Sapir-Whorf’s linguistic relativism and Chomsky’s universal grammar. BTW that goes back to the ancient Greeks. Chomsky was very much interested in knowledge and human nature, most famously through his linguistic theorizing. Universal grammar was proposed in response to the poverty of the stimulus — it’s related to Socrate’s inborn knowledge, what Chomsky refers to as Plato’s Problem. The Platonic-Chomsky approach strongly indicates an essentialist human nature with some determinist or otherwise highly constricting features.

The linguistic relativists aren’t necessarily bundle theorists. But the evidence they present offers much support for that interpretation. In particular, Daniel Everett’s observations of the Amazonian Piraha puts forth a great example, in terms of the lack of Chomky’s recursion and lack of other basic cognitive aspects such as numeracy but also in terms of demonstrating a radically different sense of self and community. This undermines many of the assumptions made and conclusions reached by studying WEIRD populations as American and European research has tended to do (WEIRD = Western Educated Industrialized Rich Democratic).

Thinking about all of this, I wonder what is your focus on aesthetics. One of the interesting observations of the Piraha is that they don’t appear to have much of an aesthetic sensibility — they lack art, storytelling, mythology, bodily adornment, decorative jewelry, etc. They also lack much in the way of abstract thought, similar to what was found among the illiterate rural population in Russia at the beginning of the 20th century. The discussion we are having right now is entirely dependent on abstractions.

It might be noted that the Axial Age was when abstract thought took hold in places like Greece. Socrates and the Sophists were among the first generations that had embraced abstract thought. That is why they could have such high level philosophical debates about knowledge, virtue, aesthetics, and on and on. In the process, they were redefining words that had been used for a long time for other purposes. The Homeric epics show traces of that earlier linguistic world and, the polytheistic mindset having dominated, some see evidence of a different kind of self. Some go so far as to argue that the bundle theory helps explain what, if we take those Greeks at their word, otherwise seems so alien.

This then brings us to the issue of arete. Instead of bundles, they would speak of gods. Their sense of self maybe was diverse, rather than unified in the way we think of it. And that effected their view of arete. Hubert Dreyfus writes In All Things:

“Homer’s epic poems brought into focus a notion of arete, or excellence in life, that was at the center of the Greek understanding of human being.6 Many admirers of Greek culture have attempted to define this notion, but success here requires avoiding two prominent temptations. There is the temptation to patronize that we have already mentioned. But there is also a temptation to read a modern sensibility into Homer’s time. One standard translation of the Greek word arete as “virtue” runs the risk of this kind of retroactive reading: for any attempt to interpret the Homeric Greek notion of human excellence in terms of “virtue”—especially if one hears in this word its typical Christian or even Roman overtones—is bound to go astray. Excellence in the Greek sense involves neither the Christian notion of humility and love nor the Roman ideal of stoic adherence to one’s duty.7 Instead, excellence in the Homeric world depends crucially on one’s sense of gratitude and wonder.

“Nietzsche was one of the first to understand that Homeric excellence bears little resemblance to modern moral agency. His view was that the Homeric world understood nobility in terms of the overpowering strength of noble warriors. The effect of the ensuing Judeo-Christian tradition, on this Nietzschean reading, was to enfeeble the Homeric understanding of excellence by substituting the meekness of the lamb for the strength and power of the noble warrior.8

“Nietzsche was certainly right that the Homeric tradition valorizes the strong, noble hero; and he was right, too, that in some important sense the Homeric account of excellence is foreign to our basic moralizing assumptions. But there is something that the Nietzschean account leaves out. As Bernard Knox emphasizes, the Greek word arete is etymologically related to the Greek verb “to pray” (araomai).9 It follows that Homer’s basic account of human excellence involves the necessity of being in an appropriate relationship to whatever is understood to be sacred in the culture. Helen’s greatness, on this interpretation, is not properly measured in terms of the degree to which she is morally responsible for her actions.

“What makes Helen great in Homer’s world is her ability to live a life that is constantly responsive to golden Aphrodite, the shining example of the sacred erotic dimension of existence. Likewise, Achilles had a special kind of receptivity to Ares and his warlike way of life; Odysseus had Athena, with her wisdom and cultural adaptability, to look out for him. Presumably, the master craftsmen of Homer’s world worked in the light of Hephaestus’s shining. In order to engage with this understanding of human excellence, we will have to think clearly about how the Homeric Greeks understood themselves. Why would it make sense to describe their lives in relation to the presence and absence of the gods?

“Several questions focus this kind of approach. What is the phenomenon that Homer is responding to when he says that a god intervened or in some way took part in an action or event? Is this phenomenon recognizable to us, even if only marginally? And if Homer’s reference to the gods is something other than an attempt to pass off moral responsibility for one’s actions, then what exactly is it? Only by facing these questions head on can we understand whether it is possible—or desirable—to lure back Homer’s polytheistic gods.

“The gods are essential to the Homeric Greek understanding of what it is to be a human being at all. As Peisistratus—the son of wise old Nestor—says toward the beginning of the Odyssey, “All men need the gods.”10 The Greeks were deeply aware of the ways in which our successes and our failures—indeed, our very actions themselves—are never completely under our control. They were constantly sensitive to, amazed by, and grateful for those actions that one cannot perform on one’s own simply by trying harder: going to sleep, waking up, fitting in, standing out, gathering crowds together, holding their attention with a speech, changing their mood, or indeed being filled with longing, desire, courage, wisdom, and so on. Homer sees each of these achievements as a particular god’s gift. To say that all men need the gods therefore is to say, in part at least, that we are the kinds of beings who are at our best when we find ourselves acting in ways that we cannot—and ought not—entirely take credit for.”

I haven’t read any Pirsig in some time. I don’t think I was a very good reader when I read him, but he didn’t make much impression. The first clause is probably more important than the second. I’ve considered rereading him, but I’m unsure.

I’d agree that arete is better thought of at “excellence”. That just would have made any discussion of the Meno into a discussion of Greek notions of morality and purpose, which would have been out of place and kind of confusing. I’ll probably keep calling it “virtue” with caveats in subsequent posts, if not simply because I’ll be talking about Aristotle and “Excellence Ethics” sounds really stupid.

I think “virtue” is fine as a translation for arete. Many (Heidegger most egregiously) avoid Latinate-English (or Latinate-German) translations for Greek ideas as though this were inherently a virtuous (haha) position, but the Romans themselves used virtus for arete pretty freely, e.g. Cicero, Sallust. We can see (along with Heidegger) the whole of Rome as part of the decline into error, declining from some Greek heyday pre-Socrates, but I don’t. (And it’s notable that Strauss, who does not see Plato as decline, does not avoid these kinds of translations, despite people accusing him of trying to make English Greek.)

The word “virtue” in English is itself more flexible than its moral meanings, anyway (e.g. “virtuous circle” has no inherently ethical meaning, and could even be called “excellence-enhancing circle” if one wished to do violence to the language).

Said Nisus: “Is it gods above that breathe
this fever in my soul, Euryalus?
or is the tyrant passion of each breast
the god it serves? Me now my urgent mind
to battles or some mighty deed impels,
and will not give me rest.

That’s probably some horrendously translated Latin, but I couldn’t find a better English translation at the drop of a hat.

I don’t follow your discussion of math whatsoever. That isn’t something I’ve studied. And so I’m not familiar with the background knowledge you are relying on. But I appreciate the question of where math comes from.

As the son of Daniel Everett, Caleb Everett spent part of his childhood among the Piraha and other tribes. It gave him firsthand knowledge how different cultures could be. He followed in his father’s footsteps and wrote a useful overview of linguistsic relativism, one of the better books available on the topic. More recently, Caleb Everett wrote a book on numbers as it is related to language and the human mind. It’s essentially about numeral relativism.

Along with some other species, humans are born with the ability of differentiating upwards of three amounts. But these are highly vague and relative, not quite being equivalent to three numerals. It’s more about comparative amounts and so the same word can be used to identify different amounts depending on what is being compared to and depending on context — such as a small pile, medium pile, and large pile of nuts. Anything beyond that is culturally determined. And some cultures lack numeracy or even terms that resemble numerals, beyond some unclear categories.

Before you can know where math comes from, you need to understand where numeracy comes from. I have no idea how this might apply to modern Western philosophy, though. But it seems to push the discussion back to a more fundamental issue involving the human nature, mind, and culture as they relate to the world.

I was reading The Jaynesian newsletter from the Summer of 2011 ( http://www.julianjaynes.org/pdf/jaynesian_volume5_issue1.pdf ). I came across two things of relevance. The first is an anecdote from Martin Seligman (taken from The Mind: Leading Scientists Explore the Brain, Memory, Personality, and Happiness, edited by John Brockman):

“When I was an undergraduate one of my teachers, Julian Jaynes, a peculiar but wonderful man, was a research associate at Princeton. Some people said he was a genius; I didn’t know him well enough to know. He was given a South American lizard as a laboratory pet, and the problem about the lizard was that no one could figure out what it ate, so the lizard was dying. Julian killed flies, and the lizard wouldn’t eat them; blended mangoes and papayas, the lizard wouldn’t eat them; Chinese take-out, the lizard had no interest. One day Julian came in and the lizard was in torpor, lying in the corner. He offered the lizard his lunch, but the lizard had no interest in ham on rye. He read the New York Times and he put the first section down on top of the ham on rye. The lizard took one look at this configuration, got up on its hind legs, stalked across the room, leapt up on the table, shredded the New York Times, and ate the ham sandwich. The moral is that lizards don’t copulate and don’t eat unless they go through the lizardly strengths and virtues first. They have to hunt, kill, shred, and stalk. And while we’re a lot more complex than lizards, we have to as well. … We have to indulge our highest strengths in order to reach eudaemonia.”

Maybe we can know ‘virtue’ in terms of human flourishing, know it by its fruit. That requires knowing human nature. And this goes back to the question of human knowledge and thought, mathematical or otherwise. What is essential versus what is learned. To get at the marrow of the essential, we need to cut away the cultural accretions of biases and assumptions. Studying ancient and non-Western societies, as Nietzsche did with the early Greeks, can help us see past our blinders. Also, as with feeding the lizard, discovery of virtues might come more from experimentation and serendipity, no matter how careful our analysis. We maybe should look for virtues in places and in ways we don’t expect them. What we think we know probably will prove wrong over time. An entirely new approach could be required.

The other thing from the newsletter is an essay. It is “Jaynes Contra Nietzsche” by James Barlow. He is a published philosopher in humanism and metaphysics. He concludes with something that speaks to what Hubert Dreyfus stated (as I shared above), in referencing Bernard Knox — that “the Greek word arete is etymologically related to the Greek verb “to pray” (araomai).” Barlow wrote:

“There is something metaphysically fundamental in the philosophizing of Nietzsche and the psychologizing of Jaynes. Nietzsche sought out a badly needed reassessment of the meaning of consciousness for the future of philosophy; Jaynes sought out a reassessment of the origin of consciousness in order to provide a rightful meaning for its place in our lives. Consciousness of consciousness is a mission and task germane to that ideal endeavor that constitutes anthropology as the study of man as man. That ideal will persist through recognition of the surprising affinities of thought shared by two epochal thinkers who lived a century apart. Perhaps Nietzsche’s fundamental, almost mythopoeic humanism is best expressed in Jaynesian terms that allude to the long, sad story of our inveterate compulsion to return to bicamerality:

” “Man appears most human to us,” wrote Nietzsche, “when he is seen on his knees, praying.” “